Chapter Closure
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Let's start by identifying the values of a, b, and c. y=2x^2-12x+6 ⇕ y= 2x^2+( - 12)x+ 6 We can see that a= 2, b= - 12, and c= 6. Recall that, if a>0 the parabola opens upwards. Conversely, if a<0 the parabola opens downwards.
In the given function we have a= 2, which is greater than 0. Thus, the parabola opens upwards and we will have a minimum value. The vertex is always the lowest or the highest point on the graph. Therefore, in this case the vertex represents the minimum value of the function.
Let's go through these steps one at a time.
The axis of symmetry is a vertical line with equation x=- b2 a. Note that the formula for the axis of symmetry is the same as the formula for the x-coordinate of the vertex. Recall that in Part B we found that the x-coordinate of the vertex equals x=3. Thus, the axis of symmetry is also 3.
The y-intercept of the graph of a quadratic function written in standard form is given by the value of c. Thus, the point where our graph intercepts the y-axis is (0,6). Let's plot this point and its reflection across the axis of symmetry.
We can now draw the graph of the function. Since a=2, which is positive, the parabola will open upwards. Let's connect the three points with a smooth curve.
